Distinct zeros and simple zeros of Dirichlet $L$-functions

Wu Xiaosheng

Distinct zeros and simple zeros of Dirichlet $L$-functions

Number Theory 2013-11-19 v4

Authors: Wu Xiaosheng

Abstract

In this paper, we study the number of additional zeros of Dirichlet $L$ -function caused by multiplicity by using Asymptotic Large Sieve. Then in asymptotic terms we prove that there are more than 80.124% of zeros of the family of Dirichlet $L$ -functions are distinct and more than 60.248% of zeros of the family of Dirichlet $L$ -functions are simple. In addition, assuming the Generalized Riemann Hypothesis, we improve these proportions to 83.216% and 66.433%.

Keywords

dirichlet l-functions distinct zeros simple zeros asymptotic large sieve generalized riemann hypothesis zero multiplicity

Cite

@article{arxiv.1206.1679,
  title  = {Distinct zeros and simple zeros of Dirichlet $L$-functions},
  author = {Wu Xiaosheng},
  journal= {arXiv preprint arXiv:1206.1679},
  year   = {2013}
}

Comments

arXiv admin note: text overlap with arXiv:1206.3737

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